Details
| Original language | English |
|---|---|
| Article number | 116828 |
| Number of pages | 17 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 422 |
| Early online date | 9 Feb 2024 |
| Publication status | Published - 15 Mar 2024 |
Abstract
The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by taking advantage of the BFPI framework. In this work, three Bayesian active learning methods are proposed under the name ‘partially Bayesian active learning cubature’ (PBALC), based on a cleaver use of the BFPI framework for structural reliability analysis, especially when small failure probabilities are involved. Since the posterior variance of the failure probability is computationally expensive to evaluate, the underlying idea is to exploit only the posterior mean of the failure probability to design two critical components for Bayesian active learning, i.e., the stopping criterion and the learning function. On this basis, three sets of stopping criteria and learning functions are proposed, resulting in the three proposed methods PBALC1, PBALC2 and PBALC3. Furthermore, the analytically intractable integrals involved in the stopping criteria are properly addressed from a numerical point of view. Five numerical examples are studied to demonstrate the performance of the three proposed methods. It is found empirically that the proposed methods can assess very small failure probabilities and significantly outperform several existing methods in terms of accuracy and efficiency.
Keywords
- Bayesian active learning, Bayesian failure probability inference, Learning function, Small failure probability, Stopping criterion, Structural reliability analysis
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 422, 116828, 15.03.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Partially Bayesian active learning cubature for structural reliability analysis with extremely small failure probabilities
AU - Dang, Chao
AU - Faes, Matthias G.R.
AU - Valdebenito, Marcos A.
AU - Wei, Pengfei
AU - Beer, Michael
N1 - Funding Information: Chao Dang is mainly supported by China Scholarship Council (CSC) . Pengfei Wei is grateful to the support from the National Natural Science Foundation of China (grant no. 51905430 and 72171194 ).
PY - 2024/3/15
Y1 - 2024/3/15
N2 - The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by taking advantage of the BFPI framework. In this work, three Bayesian active learning methods are proposed under the name ‘partially Bayesian active learning cubature’ (PBALC), based on a cleaver use of the BFPI framework for structural reliability analysis, especially when small failure probabilities are involved. Since the posterior variance of the failure probability is computationally expensive to evaluate, the underlying idea is to exploit only the posterior mean of the failure probability to design two critical components for Bayesian active learning, i.e., the stopping criterion and the learning function. On this basis, three sets of stopping criteria and learning functions are proposed, resulting in the three proposed methods PBALC1, PBALC2 and PBALC3. Furthermore, the analytically intractable integrals involved in the stopping criteria are properly addressed from a numerical point of view. Five numerical examples are studied to demonstrate the performance of the three proposed methods. It is found empirically that the proposed methods can assess very small failure probabilities and significantly outperform several existing methods in terms of accuracy and efficiency.
AB - The Bayesian failure probability inference (BFPI) framework provides a well-established Bayesian approach to quantifying our epistemic uncertainty about the failure probability resulting from a limited number of performance function evaluations. However, it is still challenging to perform Bayesian active learning of the failure probability by taking advantage of the BFPI framework. In this work, three Bayesian active learning methods are proposed under the name ‘partially Bayesian active learning cubature’ (PBALC), based on a cleaver use of the BFPI framework for structural reliability analysis, especially when small failure probabilities are involved. Since the posterior variance of the failure probability is computationally expensive to evaluate, the underlying idea is to exploit only the posterior mean of the failure probability to design two critical components for Bayesian active learning, i.e., the stopping criterion and the learning function. On this basis, three sets of stopping criteria and learning functions are proposed, resulting in the three proposed methods PBALC1, PBALC2 and PBALC3. Furthermore, the analytically intractable integrals involved in the stopping criteria are properly addressed from a numerical point of view. Five numerical examples are studied to demonstrate the performance of the three proposed methods. It is found empirically that the proposed methods can assess very small failure probabilities and significantly outperform several existing methods in terms of accuracy and efficiency.
KW - Bayesian active learning
KW - Bayesian failure probability inference
KW - Learning function
KW - Small failure probability
KW - Stopping criterion
KW - Structural reliability analysis
UR - http://www.scopus.com/inward/record.url?scp=85184519658&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2024.116828
DO - 10.1016/j.cma.2024.116828
M3 - Article
AN - SCOPUS:85184519658
VL - 422
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 116828
ER -